The rate of heat transfer in a heat exchanger is a function of several factors, regardless of whether the exchanger is for cooling purposes, for heating purposes, for transfer between fluids, or for collection and transfer of radiant energy. The rate of heat transfer is determinative of the efficiency, as well as the level or quality of performance of the heat exchanger for its intended purpose.
The conversion of radiant energy to heat involves the absorption of as many wave lengths of the radiation as possible by a black (or grey) body and transfer of heat from the black body to a working fluid such as water or air.
The rate of heat conduction, dQ/dt, from the transfer body of a heat exchanger to the working fluid is governed by the equation: ##EQU1## where Q is energy units, t is time, K is the limiting heat conductivity constant of either the fluid or the exchanger body, whichever is less, A/L is a fraction in which A is the area of contact between the transfer body and fluid and L is the length or distance between the hot surface of the heat absorbing and exchanging material and the coolest or median portion of the adjacent body of working fluid T.sub.a is the temperature of the contact surface of the transfer body, and T.sub.f is the temperature of the fluid at the aforesaid median portion. The fraction A/L is of particular interest in connection with the present application.
Specifically for a given value ot T.sub.a -T.sub.f, K is a constant characteristic of the fluid, and therefore the rate of conduction, dQ/dt is directly proportional to A/L. Consequently, a main objective of heat exchanger design is to make A as large as possible and L as small as possible. This has resulted in elaborate tubular flow arrangements, a common example being the conventional automobile radiator. In the usual case, when water or air is the working fluid, K is small and the heat exchangers rely not only on conduction, but also on natural or forced convection of the fluids to induce heat transfer.
A common feature or element of such heat exchangers is illustrated schematically in FIG. 1 of the accompanying drawings which are part of the present application, and in which the fluid is made to circulate within a metallic tube or conduit 1 which is attached to the surface of a metallic member or fin 2. Heat exchange, in this instance, depends on conduction of heat to or from the fluid to the surface of the transfer member or fin 2. It will be understood that, for industrial use, many hundreds or thousands of such tubes would be utilized. When such an exchanger is used as a solar collector, the surfaces facing the sun are made black by painting, oxidizing, etc. Thermal insulation for such an exchanger from its surroundings is provided by one or more transparent covers 3, 4, and a backing 5.
Another prior art form of tubular heat exchanger is schematically illustrated in FIG. 2 of the drawings. In this form, the heat transfer takes place between fluids circulating in the inner conduit 6 and the coaxial outer conduit 7. When this form is used as a solar collector, the working fluid circulates within a blackened inner conduit 6, made of metal, which is placed within a transparent tube 7, the space between the conduit 6 and tube 7 being evacuated to reduce heat loss by conduction and convection.
Typically, the radii of tubes used in solar collectors are of the order of 1 cm. Therefore, A amounts to approximately 6 cm.sup.2 for each lineal centimeter of tube. Since L is approximately 1 cm, A/L is 6 cm per unit length of tube.
The art has also addressed itself to non-metallic heat exchangers or solar collectors. Representative of the current state of the art is the recently issued Rice et al. U.S. Pat. No. 4,310,747 and the prior art Harvey U.S. Pat. Nos. 4,082,082 and 4,129,117.
Rice et al. disclose a heat transfer device in which the heat source is either an electrical resistance element or, alternatively, solar energy, or possibly both in combination. The same heat exchanging material is utilized for both sources of energy and consists of a baked, skeletal, porous, vitreous carbon structure containing multi-directional, interconnected carbon strands having electrical continuity. The starting material for this skeletal network is a flexible polyurethane resin reticulate structure which is transformed into non-crystalline amorphous carbon. Rice et al. describe this porous body as having a density of about 0.05 g/cc. Inasmuch as amorphous carbon has a density of about 2.0 g/cc, it is evident that the composite body is highly porous and would have a ratio of carbon to space (or flow passages) on the order of 1:40, providing a relatively small carbon mass and contact area for heat transfer contact with the working fluid although, conversely, providing a relatively large area of flow passageways for the fluid.
It is also to be noted that vitreous amorphous carbon such as utilized by Rice et al. not only has significant electrical resistivity to achieve the patentee's objective of providing an electrical resistance heating element, but also has a relatively low value of thermal diffusivity or conductivity on the order of 1.0.times.10.sup.-3 cm.sup.2 /sec, which is significantly lower than the thermal diffusivity of the metals, such as copper, used in tubular heat exchangers, which is on the order of 1.0 cm.sup.2 /sec.
The two Harvey patents disclose a solar collector utilizing a particulate of fibrous, blackened exchanging material which is characterized by the patentee as having "high solar energy absorption and low thermal diffusivity (e.g., preferably below 2.5.times.10.sup.-3 cm.sup.2 /sec)." A variety of materials are listed, with carbon-filled, high density polyethylene being a preferred example. The particle size is described as a mean diameter in the range of 1 to 10 mm, preferably 3 to 4 mm. The particles are deliberately loosely packed to permit them to move or circulate freely in response to flow of the working fluid, presumably to permit sequential exposure of the particles to the unidirectional solar radiation, as they are not packed to be thermally conductive with each other.
Neither Harvey nor Rice et al. disclose any performance data for their solar collectors, but both mandate very low values of thermal conductivity for the absorber material, as this characteristic is necessary to achieve the result the patentees seek. In Harvey, low thermal diffusivity of the particles is desirable to localize heat absorption at the surface of the moving particles and increase the exposed particle skin temperature by inhibiting heat transfer to the interior of the particle. In Rice, very low thermal diffusivity is taught to achieve a carbon strand having high electrical resistivity for resistance heating.
The prior art tubular metal heat exchangers, particularly those used industrially or in chemical processing, utilize solid metal heat exchange bodies which have relatively high thermal diffusivity, but are unduly restricted in area of contact with the working fluid by reason of mechanical design limitations.
The prior art non-metallic collector of the Harvey patents attempts to enhance the area of heat transfer contact by the use of carbon-containing particles for the heat exchange medium, but deems it necessary and desirable to sacrifice good thermal diffusivity to do so. The same is true of the more recent Rice disclosure. Both of these disclosures could have limited usefulness in intermittent, low-demand situations where a low rate of heat transfer is acceptable and adequate, as for supplementary hot water heating for home use.
The present invention is directed to overcoming the limitations of prior art heat exchangers, both the metallic tubular and non-metallic, by significant and radical improvement of the rate of heat transfer, particularly in the continuous, high-demand industrial and nuclear applications.